What is on the menue to hunt,if elk are you need to consider enough gun.
That means starting at IMO.270 caliber or larger.
When men hear that you are looking for a gun for the " other" they go small frame,and caliber to match.

How much shooting dose she do,has she hunted before?These all need to be answered.

If this is a surprise,make sure it is one she wan' ts,it' s kinda of like buying blender for her birthday they tend to frown on that.

My wife likes to her .280 Rem in a Mountain Rifle,light fits her well and mild recoil.
Another good maker would be Winchesters Classic Compact in 7mm-08,or Browning A-Bolt Micro Hunter .260 or .308.
It all depends on what you wish to hunt.